I'm sorry you feel so down.
You need a meno specialist not a gynaecologist. But before you think of seeing anyone else it might be wise to do some research. Because there isn't a testosterone product that's licensed for women in the UK whoever prescribes it is responsible for your safety. It might be that there's a good reason she won't prescribe it to someone with a high BMI, it might be more dangerous for you than for others. If it is you may have to accept you either don't have it or reduce your BMI. If it isn't you can argue your case and she can explain WHY she won't prescribe it, and at least you'd have a chance of someone else prescribing it.
You say your life is flat and joyless. I'm not sure if testosterone will fix that. For me it has helped libido (from zero to very low, nothing like what it used to be), stamina and muscle strength (used to pull them frequently). Mood was helped by oestrogen.
Not all meno specialists will prescribe testosterone (to anybody) so do ask questions before you spend any more money.
Great post sheila99
Nik2502 - High BMI of itself is not a contra-indication to HRT but depending on your age and where in menopause you may be at greater risk from stroke etc - depending on your general health and other risk factors eg BP and cholesterol, whether you smoke, exercise well, diet etc. However transdermal HRT is not associated with greater stroke risk so you should be able to be prescribed this - if no other contra-indication and depending where in menopause you are, and what your natural periods are doing?
You would not want to have tesosterone without oestrogen anyway as you could tip the balance to become T dominant and then may get androgenic sdie effects.
If you are on other medication - this can also depress libido eg some ADs and others. Oral HRT also can depress libido so transdermal ( patches or gel) would also be the way to go.
You could argue that once you have improved your menopausal symptoms ( flushes and sweats? Mood?), you will be in a better position to take positive steps to reduce your BMI which of course is desirable for your long term health.
Not sure if this has been mentioned but have you also had your thyroid function checked? Many women put on weight at this point in their life due to slowing of the metabolism but also some women like SueLW as she has said - develop underactive thyroid which increases weight gain and is very poorly recognised and treated.
Hope you find a solution!
Hurdity x